Most employers have adjusted to dating among employees, but they still remain skittish about it. Messy breakups tend to affect worker productivity. Dalliances between superiors and underlings can gouge employee morale.
Firm policies on employee romance vary from firm to firm. Some companies require that you report when a relationship has begun, especially if one of you is in a supervisory role. Get a sense of the rules, written and unwritten, at your company.